Finite Group Databasebeta

C2×Q16×D43 #14583674

order2752
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q16×D43

Splittings

FittingC2×Q16×C43 ⋊ C2
SylowC43 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC22D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
FittingC2×Q16×C43C2
socleC22×C43C2×D4
prime radicalC22×D43D4
hypercenterC2×Q16D43
hypocenterC43C22×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1324);